A perfect post-filtering technique should not alter the formant information and should attenuate null information in the speech spectrum in order to achieve noise reduction and hence produce better speech quality. Conventionally, time-domain post-filtering techniques use modified LPC synthesis, inverse, and high pass filters that are derived from an LPC spectrum and are configured by the constants: .alpha. (for modified synthesis filter), .beta. (for modified inverse filter) and .mu. (for high pass filter). See, Juiun-Hwey Chen, Allen Gersho "Adaptive Post-filtering For Quality Enhancement of Coded Speech", IEEE Trans. Speech & Audio Proc., vol. 3, no. 1, pp. 59-71, 1995. Such a filter has been used successfully in low bit rate coders, but it is very hard to adapt the coefficients from one frame to another and still produce a post-filter frequency response without spectral tilt. The result is time-domain post-filtering which produces varying and unpredictable spectral tilt from one frame to another which causes unnecessary attenuation or amplification of some frequency components, and a muffling of speech quality. This effect increases when voice coders are tandemed together. However, it is very hard to adapt these coefficients from one frame to another and still produce a post-filter frequency response without spectral tilt. Conventional time-domain post-filtering produces varying spectral tilt from one frame to another affecting speech quality.
Another problem with conventional time-domain post-filtering is that, when two formants are close together, the frequency response may have a peak rather than a null between the two formants hence altering the formant information. Yet another effect is that in the original speech, the first formant may have a much higher peak than the second formant, however, the frequency response of the post-filter may have a second formant with a higher peak than the first formant. These phenomena are completely undesirable because they affect the output speech quality.
Another approach of designing a post-filter is described by R. McAulay, T. Parks, T. Quatieri, M. Sabin "Sine-Wave Amplitude Coding At Low Data Rates", Advances in Speech Coding, Kluwer Academic Pub., 1991, edited by B. S. Atal, V. Cuperman and A. Gersho, pp. 203-214. This technique has produced good performance without spectral tilt, but it can only be used in sinusoidal based speech coders.